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Anomaly detection is an important problem that has been well-studied within diverse research areas and application domains. The aim of this survey is two fold, firstly we present a structured and comprehensive overview of research methods in deep learning-based anomaly detection. Furthermore, we review the adoption of these methods for anomaly across various application domains and asess their effectiveness. We have grouped state-of-the-art research techniques into different categories based on the underlying assumptions and approach adopted.  Within each category we outline the basic anomaly detection technique, alongwith its variants and present key assumptions, to differentiate between normal and anomalous behavior. For each category we present we also present the advantages and limitations and discuss the computational complexity of the techniques in real application domains. Finally, we outline open issues in research and challenges faced while adopting these techniques.

